High resolution and high sensitivity friction force microscopy (FFM) is used to distinguish between different crystallographic domains of standing up molecular configurations of self-assembled alkanethiols partially covering Au(111) surfaces. We propose two suitable methods to decipher structural domains of the same configuration depending on the two-dimensional (21)) symmetry of the organic adlayer. For the hexagonal root 3 x root 3)R30 degrees where no differences among equivalent domains are expected in lattice-resolved scanning force imaging, different molecular domains however can be observed in lateral force images because of the friction asymmetry caused by domains presenting different relative orientations between the molecular tilt direction and the tip scanning direction. Since no lateral packing anisotropy is expected in this close-packed configuration, no friction anisotropy however is observed. Conversely, because of its rectangular space group symmetry, lattice resolved stick-slip imaging is enough to solve between the existing domains for the (2 x,root 3) rectangular configuration.